G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari. A clustering technique for the identification of piecewise affine and hybrid systems. Automatica , 39:205--217, 2003.
We propose a new technique for the identification of discrete-timehybrid systems in the Piece-Wise Affine (PWA) form. This problemcan be formulated as the reconstruction of a possiblydiscontinuous PWA map with a multi-dimensional domain. In order toachieve our goal, we provide an algorithm that exploits thecombined use of clustering, linear identification, andpattern recognition techniques. This allows to identify both the affinesubmodels and the polyhedral partition of the domain on which eachsubmodel is valid avoiding gridding procedures. Moreover, the clustering step (used forclassifying the datapoints) is performed in a suitably definedfeature space which allows also to reconstruct different submodels thatshare the same coefficients but are defined on different regions.Measures of confidence on the samples are introduced and exploitedin order to improve the performance of both the clustering and thefinal linear regression procedure.